The effect of quantitative easing on the term premium of German bonds

(1)

The Effect of Quantitative Easing on

the Term Premium of German Bonds

Bachelor Thesis

Armen Hachijan 10419039

Supervisor: Egle Jakucionyte

January 2016

Abstract

Short-term interest rates have hit very low levels in the Eurozone, where yields of German bonds have been negative for the past 16 months. The ECB could not boost spending in the economy anymore by lowering short-term yields and therefore started targeting long-term yields in March 2015. This paper tries to examine what has been the effect of quantitative easing (QE) on the term premium of German bonds. For that reason a regression is run of the term premium on a set of variables including QE. Statistically significant results show that the QE policy indeed succeeded in lowering the term premium of German bonds.

Keywords: Quantitative Easing (QE); Term premium; German bonds

JEL Classification: E43, E52, G12

(2)

Introduction

Central banks typically target short-term interest rates by buying short-term government bonds. Lower interest rates make borrowing cheaper and therefore more money will be spent in the economy. However, during the most recent financial crisis these short-term rates are already approaching zero, so the policy loses its effectiveness. This can also be concluded by observing the inflation levels in the Eurozone from 2012 to 2014. These levels have declined steadily since 2012 and even became negative at the end of 2014, suggesting that conventional monetary policy did not succeed in increasing spending.

Quantitative Easing (QE) is an unconventional monetary policy in which a central bank buys instead long-term financial assets (which have higher yields than short-term assets) in the open market. By buying these assets, it increases the price and therefore lowers the yield. With lower yields, borrowing becomes less expensive and as a consequence more money will be spent in the economy, stimulating economic activity (Bernanke and Reinhart, 2004). QE can affect the economy through different channels. These are the signaling channel, duration risk channel, liquidity channel, safety premium channel, prepayment risk channel, default risk channel, inflation channel, and portfolio balance channel.

The results of QE are socially very relevant since a higher amount of money spent in the economy leads firms to expand their production. For this expansion in production a higher amount of labor is needed and as a result unemployment decreases. The QE policy is in an early stage yet since the ECB has started to buy public sector securities in March 2015 only. Therefore no research is available thus far on the effects of the policy. This paper for that reason tries to make a beginning in determining the effects of the policy in Europe’s economically most powerful nation Germany and targets the term premium, which is a part of the long-term yield. The term premium (also risk premium) is the extra return that investors require for holding assets that have more interest rate risk (such as long-term bonds). Long-term yields consist of short-term rate expectations and the term premium (there is virtually no default risk for government bonds of an economically powerful nation such as Germany). The ECB’s QE policy will most likely have a greater effect on the term premium rather than the short-term rate expectations (see research method). Therefore estimating the term premium can explain a great part in the overall long-term yield. Subsequently, the question that this paper intends to answer is what the effect of QE is on the term premium of German bonds. Control variables include the unemployment gap, CPI inflation, long-run inflation disagreement, six-month realized daily volatility of the on-the-run ten year government bond, net public-sector supply of longer- term debt securities, and assets bought by the ECB under the Public Sector Purchase Programme (PSPP), which is the QE variable. An additional dummy variably will be used to capture the effect of the QE announcement in January 2015.

The QE policy has been used before in powerful economic nations. Japan implemented the policy in the early 2000’s, when short-term interest rates were very low there. More recent are the U.S. and the United Kingdom, who started buying long-term assets in 2008 and 2009 respectively. Research from Oda and Ueda (2005) showed that long-term yields in Japan indeed dropped as a result of QE. Joyce, Tong, and Woods (2011) reach the same conclusion for the United Kingdom and Gagnon et al. (2010) show that QE dropped long-term yields in the U.S. as well. The term premium is a component of long-term

(3)

yields, therefore it is expected that the term premium will indeed fall as well in Germany, ceteris paribus.

This paper starts with discussing the various channels through which QE works in the economy. Next, the empirical results in Japan, United Kingdom and U.S. will be reviewed and in conclusion the results of the empirical model will be covered. At the end of the paper an appendix with regression models and various statistical tests can be found.

Literature review

Channels of QE

This section discusses possible channels through which QE may have an effect on the economy in the countries where QE was implemented. The following analysis of channels comes from Krishnamurthy and Vissing-Jorgensen (2011), who evaluate the effect of the QE1 (2008-2009) and QE2 (2010-2011) programmes in the U.S. The channels listed below are mostly theoretical predictions of the possible channels of QE according to the classification of the authors. The QE programme is in an early stage in the Eurozone countries, so which channels have the most effect on general welfare have to be determined yet. The channels listed below are mostly general ex-ante predictions. The authors list the following possible channels through which QE may work.

• Signaling channel. This is the channel through which the announcement of the central

bank to buy long-term assets in the future signals information about the central bank’s desire to keep the rates of these assets low. Since investors expect that rates will decrease, the market mechanism automatically incorporates this in the prices and thus the yields of these assets. According to Eggertsson and Woodford (2003) though, the signaling effect can keep expectations of long-term rates low only if the public believes that the government will continue the programme after the economy recovers. The central bank thus has to send a credible signal and this can according to Clouse et al. (2000) be achieved by buying a high amount of long-term assets during QE. This way it is less likely for the government to raise rates afterward by selling long-term assets because then it takes a loss (since higher yields mean higher interest rate costs for the issuer). Moreover, bond market rates of all maturities get affected by the signaling channel according to the expectations hypothesis. The expectations hypothesis states that the future long-term rate is determined by the current rates and the future expected short-term rates, which according to Krishnamurthy and Vissing-Jorgensen (2011) will be kept low as a policy instrument.

• Duration risk channel. Duration risk measures how sensitive bond prices are to a change

in interest rates. Duration is measured in years, where a higher amount of years means a greater interest rate risk (Mishkin, Matthews, and Giuliodori, 2013). The central bank buys long-term assets from the public, so the amount of duration risk in the hands of the public decreases (less long-term assets) and long-term yields compared to short-term yields thus decrease (Vayanos and Vila, 2009). A possible problem might be that the assets bought are only Treasuries and not all long-term assets. Greenwood and Vayanos (2010) show empirically that a decrease in the relative supply of long-term Treasuries compared to short-term Treasuries indeed affects the spread between their rates

(4)

term yields decrease), but this also only contains Treasury bonds and not all long term assets. Gagnon et al. (2010) however accept the view of Greenwood and Vayanos (2010) for the general long-term asset market and Krishnamurthy and Vissing-Jorgensen (2011) follow Gagnon et al. (2010) in this view. Therefore Krishnamurthy & Vissing-Jorgensen (2011) predict that QE decreases the yield on all long-term assets (so not only Treasuries) and the effects are larger for assets of longer duration.

• Liquidity channel. With the implementation of QE, the government buys long-term

assets from investors and pays with money to acquire them. Thus, the amount of liquidity in the hands of investors increases. Treasury bonds are very liquid assets since they are intensively traded on the market. Therefore investors pay a higher price for these liquid assets when there is less liquidity in the economy. When the amount of liquidity in the hands of investors rises, they are in less need of it and are therefore willing to pay a lower price for the most liquid assets (Treasury bonds). QE thus raises yields on the most liquid assets relative to less liquid assets through this channel (Krishnamurhy and Vissing-Jorgensen, 2011).

• Safety premium channel. The safety premium channel shows the higher price that

investors are willing to pay for long-term assets that are safe. In an earlier paper, Krishnamurthy and Vissing-Jorgensen (2010) consider safe assets (i.e. relatively low default risk) assets that are ranked higher than Baa. The Consumption Capital Asset Pricing Model (C-CAPM), which is an extension of the CAPM (here an investor’s consumption of goods is also included as opposed to CAPM) shows the negative linear relationship between a bond’s price and its probability of default. According to the authors the relationship between a bond’s price and its probability of default is not linear anymore for bonds ranked higher than Baa since investors are willing to pay extra for assets that they consider as long-term safe. Because QE decreases the supply of these bonds, investors are willing to pay a higher price for these bonds compared to the linear relationship of the CAMP. The spread between these yields (which rises since yields on long-term safe assets decrease more than proportionally compared to C-CAPM) is considered as the safety premium. The prediction of Krishnamurthy and Vissing-Jorgensen (2011) is thus that QE effects of lowering yields are larger for the safest assets and smaller or even none on Baa bonds through this channel.

• Prepayment risk premium channel. Prepayment risk is the risk borne by investors when

the borrower returns cash payments (and principal) earlier than in the designated time period (this occurs mostly with MBS’s). Investors therefore do not get the interest that they were supposed to get if the cash payments would be returned on the designated time and they demand a positive prepayment risk premium for this. Gabaix, Krishnamurthy, and Vigneron (2007) state that the amount of prepayment risk depends on the total amount of prepayment risk that is in the market (held by investors). QE1 in 2008-2009 purchased MBS’s and thus the amount of prepayment risk in the market decreased and the implication was that the prepayment risk premium decreased. Since the prepayment risk premium is a part of the yield of MBS’s, these MBS purchases lower MBS yields compared to other bond yields. The demand for other bonds, such as corporate bonds may rise and accordingly make it cheaper for corporations to borrow. These corporations can then inject more money in the economy and therefore overall welfare rises (Krishnamurthy and Vissing-Jorgensen, 2011).

• Default risk channel. Default risk is defined as the risk that the issuer is unable or

unwilling to make payments or pay off the final amount of the bond to the lender 4

(5)

(Mishkin, Matthews, and Giuliodori, 2013). Corporations have for example a higher risk of default than governments, because the government can always levy taxes if it cannot repay its debt. Krishnamurthy and Vissing-Jorgensen (2011) explain that if QE succeeds in stimulating the economy (by lowering yields of long-term assets, which makes borrowing and thus spending cheaper and/or by increasing the money supply in the economy, which also stimulates spending), then the default risk of corporate bonds will fall in the following way. When economic activity is stimulated, corporations can sell higher amount of units and/or raise prices and thus earn a higher profit. A higher profit for corporations lowers their default risk and hence the yields on their debt. The difference of this channel compared to the safety premium channel is that the absolute yields on the safe long-term asset are affected through the safety premium channel. Assets that are not considered safe by the authors (Baa and lower) are instead affected through this channel. If QE worked through both of these channels, then this would mean that the yields on all assets (safe and not safe assets) would decline and borrowing would become cheaper for both types of borrowers, thus stimulating spending in the economy.

• Inflation channel. The central bank increases the money supply in the economy with QE

by buying long-term assets and paying with money. If there is more money in the economy, agents have more money to spend and this increases inflation. This information is known to the public and hence inflation expectations are formed. Krishnamurthy and Vissing-Jorgensen (2011) researched empirically whether inflation expectations have risen and by how much during QE1. They did this by looking at the 10- year zero coupon inflation swaps and by looking at the difference between nominal bond yields and Treasury Inflation Protected Securities (TIPS). Both financial instruments are used to transfer inflation risks between two parties. With a zero coupon inflation swap investors get a lump-sum payment at the end of the maturity and payments of TIPS are paid semiannually. The market mechanism determines the rates on these financial instruments and investors’ inflation expectations are thus incorporated in these rates. The authors considered five Federal Open Market Committee (FOMC) announcements from 2008 to 2009 and used the 10- year zero coupon inflation swap as a proxy for inflation expectations over the next 10 years. They observed that the 30- year swap rate increased by 35 basis points and the 10- year swap rate increase by 96 basis points, suggesting that inflation expectations increased. They also observed the difference between nominal bond yields and TIPS as another measure of inflation expectations. Using the same five FOMC announcements, they found that the difference between 10- year nominal bonds and 10- year TIPS increased by 117 basis points and the equivalent for a 5 year horizon was an increase of 82 basis points. These two different measures show that indeed inflation expectations increased because of the Fed’s QE. It is therefore likely that inflation expectations in Germany will rise as well as a consequence of QE.

• Portfolio balance channel. In a speech in Wyoming (2012), Ben Bernanke stated that QE

purchases work primarily through the portfolio balance channel. Portfolio balancing is choosing a mix of different securities for one’s portfolio. The Fed assumes that different securities in one’s portfolio are not perfect substitutes, so changes in one type of asset (such as yield or riskiness) may change the composition of the entire portfolio since investors would substitute assets. For example, when the FED buys MBS’s from the public, it raises the price and reduces the yield on these assets. Investors can therefore

(6)

decide to buy different types of assets instead of MBS’s, since the relative yield of those assets compared to MBS’s has improved. Investors will for example substitute MBS’s for long term corporate bonds. This way the demand for long-term corporate bonds rises and the yield on these bonds decrease, making it cheaper for corporations to finance their operations and thus stimulate the economy.

Through which of these channels QE has the highest effect on the economy in Germany has to be determined yet when the QE programme in the Eurozone can be researched empirically. It is in addition not determined yet through which of these channels QE has an effect on the term premium of German bonds, but in the research method section a number of predictions are made on which of the explanatory variables have an effect on the term premium.

Literature review

The first economic superpower that has implemented QE is Japan in the early 2000’s. Japan had used an approach where they combined a Zero Interest-Rate Policy (ZIRP), where nominal short-term interest rates are kept at zero with QE. The goal of QE then is to increase the monetary base and lower yields of medium and long- term yields .Results of the analysis of Oda and Ueda (2005) show that the ten-year interest rate in 2001-2003 was on average 1.33%, as opposed to 1.91% in the preceding three years. The five and three year-interest rates fell on average as well, though not as much as the ten-year interest rate (0.54% and 0.43%). The authors came to these results with a backward-looking empirical model from 1995 to 2004 using equations for aggregate demand and supply and a modified Taylor rule for monetary policy. The authors examined the dates of announcements of the QE programme in Japan using a maximum likelihood function. By looking at the dates and the interest rate changes, they conclude that QE worked through the signaling channel in reducing those rates. Bowman, Cai, Davies, and Kamin (2011) identified the credit channel through which QE worked in Japan. This is a general monetary policy (not only QE) channel through which banks obtain liquidity. By buying long-term assets from commercial banks, banks obtain more money and increase their lending. The authors state that bank liquidity had a robust, positive, and statistically significant effect on lending. This suggests QE has increased the amount of loans in the economy. However, this effect was quite small since banks decided to keep much of the liquidity as reserves. Banks decided in addition to reduce interbank lending, which offset some of the effect of QE. According to that same paper, ‘’most analysts agree that the QE program did not succeed in stimulating aggregate demand sufficiently to overcome persistent deflation’’. This can be seen by looking at the core CPI inflation and GDP in the period after the small recession in early 2002. The authors show that even though GDP has grown by approximately 100 basis points in that period, inflation did not succeed in becoming positive.

QE was also implemented in the United Kingdom during the most recent financial crisis. Over the period March 2009 to January 2010 government bonds were purchased in the United Kingdom. There is considerable uncertainty about the magnitudes of these purchases, but according to Joyce, Tong, and Woods (2011), evidence suggests that QE had significant effects on the economy through channels such as policy signaling, portfolio balance, liquidity premia, and bank lending. They come to this evidence by comparing gilt (low risk government bonds) yields before and after announcements of the Bank of England.

(7)

They find for example that from January 2009 to February 2010 gilt yields fell on average just under 100 basis points due to the Bank of England’s announcements of the QE program. The macroeconomic impact of these purchases is considered by Nelson (2012). In 2008, the index of real GDP (which is nominal GDP/CPI) was 0.989 (with 2007 as base year) and nominal GDP was 1.020. Real GDP dropped in 2009 even further to 0.945 and nominal GDP also dropped to 0.992. With the implementation of QE the economy seemed to have recovered in 2010: real GDP increased to 0.962 and nominal GDP to 1.037. These numbers show that QE succeeded in increasing output.

Gagnon et al. (2011) found that Large-Scale Asset Purchases (LSAP’s) in the U.S. since 2008 led to long-lasting reductions in longer-term interest rates on a range of securities. They used a regression to estimate the term premium of long-term assets using factors related to the business cycle, uncertainty about economic fundamentals and QE. Securities that that were not a part of the program were affected as well as a result of reduced default risk (see under ‘’default risk channel’’ in the previous subsection how these securities got affected). Publicly and privately held Treasury securities with at least one year to maturity, Treasury securities held in the Fed’s System Open Market Account (SOMA) portfolio, and U.S. debt securities held by foreign official agencies with at least one year to maturity are examples of affected securities. These reductions come from decreases in the risk premium, including term premia. Christensen and Rudebusch (2012) also found evidence that longer- term interest rates (government bonds in this case) in the United States decreased. They explain in a theoretical approach that U.S. Treasury yields declined due to lower policy expectations, rather than the term premium, as stated by Gagnon et al. (2011).They come to this conclusion by making use of close substitutes to U.S. Treasuries. For example the OIS rates represent average expectations for the effective federal funds rate over the period November 2008 to November 2009. The spread between Treasury and OIS rates during that period were very small and thus the authors state that there is a common factor behind the decline in the Treasure yields and OIS rates. To support their analysis they also use corporate bonds and interest rate swaps tied to the U.S. dollar LIBOR. The similar reaction of these interest rates to LSAP announcements suggests that there is little market segmentation during this period. On the basis of these similarities the authors conclude that there is one common channel for the declines in these rates and that is the signaling channel. In the U.S. the policy of QE also had positive effects on output. Nelson (2012) observed that here too real GDP and nominal GDP increased in 2010 compared to 2009. Real GDP in 2009 was 0.991 and nominal GDP was 1.035 (both with base year 2007). In terms of real GDP, it can be seen that the recovery in the U.S. was even larger compared to the United Kingdom.

The above listed QE programmes show that the desired effect on long-term asset prices has been achieved. Fawly and Neely (2013) agree on the positive effect of the QE purchases on asset prices, but they point out that it is not possible to say with certainty whether QE had also an impact on other (and which) parts of the economy. What can be said with certainty is that GDP in all three countries has risen during the QE programmes and this is a positive overall effect on the economy.

(8)

Research method

This paper attempts to examine what the effect of QE is on the term premium of German bonds. Germany is chosen because it is the economically most powerful nation in the Eurozone. The research method of this paper follows the approach of Gagnon et al. (2011), where the changes in the term premium are explained by factors related to:

• The business cycle

• Uncertainty about economic fundamentals • Public sector supply of long-term debt

The explanatory variables in the regression model reflect these factors. The analysis in Gagnon et al. (2011) was conducted for the first round of the QE program in the United States starting in 2009. Long-term yields consist of two components according to the liquidity premium theory. The first component is the expected future short -term rate. If people expect future short-term rates to be high, then they might substitute long-term bonds for shorter-term bonds. This affects yields on long-term bonds negatively, since the demand for those bonds falls. The second component is the term premium (also called risk premium). The term premium is the extra return that investors require for holding assets that have more interest rate risk (such as long-term bonds) than short-term assets. These assets bear more interest rate risk because there is a higher maturity on them, so investors want to be compensated for that (Mishkin et al., 2013). There is virtually no default risk for long-term government bonds of wealthy nations such as the U.S. and Germany, so this is not a component of long-term government bond yields for those nations. The term premium is a part of the overall bond yield, so a decrease in the term premium will lead to a decrease in the long-term bond yields ceteris paribus. Since the ECB has not announced direct messages to the public about its future short-term rates (increases or decreases), it is likely that the term premium will capture the largest part of the overall yield of long-term bonds. This is also stated by Gagnon et al. (2010) for the case of the U.S. They authors explain that the Fed did not use the LSAP programme as an indicator that the future short-term rates will be kept low. Following the approach of Gagnon et al. (2011), this paper will run an Ordinary Least Squares (OLS) to estimate the QE effect on the nominal ten-year term premium of government bonds in Germany. Control variables include unemployment gap, CPI inflation, long-run inflation disagreement, six-month realized daily volatility of the on-the-run ten year government bond, net public-sector supply of longer- term debt securities, and assets bought by the ECB under the Public Sector Purchase Programme (PSPP), which is the QE variable. The regression uses monthly data from December 2005 until December 2015. Most of the data is downloaded from the database of Bloomberg. Additional sources are the ECB database, the Deutsche Bundesbank database, OECD, and the World Bank. The following variables are used in the model.

• Nominal ten-year yield term premium. This is the dependent variable that the model

tries to explain. In the definition above, long term yields were decomposed into expected future short-term rates and a term premium. So this must mean that long term yields minus expected future short-term rates equal the term premium. The problem with expected future short-term rates is that it is impossible to forecast them since it is not possible to measure these expectations. Swanson (2007) discusses a survey-based measure to get information about people’s future short-term rate expectations. 8

(9)

Unfortunately there are a lot of problems with this kind of measure, for example only rough estimates are reported by respondents. Other measures are complicated statistical models which are beyond the scope of this paper, such as the Kim-Wright model. Therefore this paper uses a proxy for expected future short-term rates and these are the ex-post short-term rates, as proposed by Kim (2007). The ex-post short- term rates will not reflect the future short rate expectations perfectly, but this proxy is the most reliable since investors’ expected future short-term rates might be incorporated in the yields through the market mechanism. In this paper the nominal ten-year term premium will be defined as the yield on a 10-year government bond subtracted by the yield on a 2-year government bond. By doing that, the term premium gets isolated. Daily data from the database of Bloomberg is used and averaged to monthly data by taking the average of the daily data.

• Unemployment gap. The difference between the actual unemployment rate and the

natural rate of unemployment. Monthly data is available on the unemployment rate in Germany. For the natural rate of unemployment the non-accelerating inflation rate of unemployment (NAIRU) is used. The NAIRU is the rate of unemployment at which inflation is constant (Mishkin et al., 2013). The NAIRU uses the concept of the Phillips curve, which states that there is a negative relationship between the actual unemployment rate and inflation (when the NAIRU is constant). The idea behind the Phillips curve is that when unemployment decreases, consumers can spend more money in the economy (since they have higher income) and demand for goods increases. A higher demand for goods pushes prices up and causes inflation. So when the gap between the actual unemployment rate and the NAIRU increases, this should pull down inflation. According to Bernanke (2015), lower inflation keeps long-term interest rates low, since lenders are not demanding higher returns to compensate for losses in purchasing power (Berk and DeMarzo, 2014), but it is not evident that the term premium component is responsible for this effect. According to Adrian et al. (2013) of the Federal Reserve Bank of New York the term premium instead rises when unemployment rises since people demand a higher risk premium (which includes the term premium and default premium for example) in ‘’bad times’’ (i.e. when unemployment is high), because they are less certain that they will get their investment back. So it is expected that the term premium will rise as a consequence of a higher unemployment gap. Estimations of the NAIRU are taken from the database of the Organization for Economic Co-operation and Development (OECD). Data on the NAIRU is only yearly available here, but this should not be a problem since the NAIRU estimates are quite close to each other through the years. The value of 2015 is yet missing, but since this variable is a slowly adjusting variable, the rate of 2014 will be used as a proxy for the rate of 2015. Also, since the data is established for the entire year, the monthly unemployment gap will be calculated. This will be done by taking an average of two surrounding yearly rates. Data on the actual unemployment rate is downloaded from the database of Bloomberg.

• CPI inflation. The change in the Consumer Price Index (CPI) in Germany. The CPI can be

used as a proxy for inflation uncertainty because a rise in current inflation rates can raise uncertainty about increases in future inflation rates. Decisions about future inflation rates then are made on past inflation rates, as stated by the adaptive expectations hypothesis (Mishkin, 2013). Ball (1990) explains that when inflation is low, the public believes that monetary policy will keep it low. When inflation is high however,

(10)

policymakers might decide to lower inflation, which might cause a recession. Since what happens in this situation depends on the policy ideals of policymakers, the public is not sure what will happen and thus inflation uncertainty arises. Wright (2008) found a positive relationship between inflation uncertainty and the term premium. He explains that long-term bonds are riskier than short-term bonds because inflation reduces the value of their bonds over a longer period compared to short-term bonds. When investors are uncertain about inflation, they will demand a higher term premium to compensate them for this risk. Therefore it is expected that the coefficient of the CPI inflation in this paper will be positive. Monthly data on the CPI inflation is downloaded from the database of Bloomberg.

• Long-run inflation disagreement. The EUR Inflation Swap Rate is used as a proxy for

inflation expectations of investors. An inflation swap is a security that transfers inflation risk between parties. The interest rate on inflation swaps reflect agents’ expectations about future inflation and thus can be used as a proxy for inflation expectations. The EUR inflation rate thus captures the inflation expectations of residents in the Eurozone and this is used as a proxy for the inflation expectations in Germany. The mechanism through which inflation expectations have an effect on the term premium is similar to the previous explanatory variable: higher inflation expectations are likely to raise the term premium (see the previous point for explanation). Daily data is downloaded from the database of Bloomberg and transformed into monthly data by taking an average of the daily values.

• Six-month realized daily volatility of the on-the-run ten year government bond. Data of

the realized volatility of the most recently issued (‘’on-the-run’’) ten-year government bond in Germany. This variable can as well be used as a proxy for interest rate uncertainty because of the volatility component. Investors are generally risk-averse and thus prefer bonds with lower volatility. When bonds are more volatile, investors demand a higher risk premium for bearing this risk (also term premium) and thus the yield on these bonds rises. Thus it is expected that the coefficient of this variable should be positive as well. Daily data of the most recently issued ten-year government bond is downloaded from the database of Bloomberg. The data is averaged into monthly data by taking an average of the daily rates.

• Net public-sector supply of longer-term debt securities. This is debt issued by the central

government and all other governmental institutions (such as the state government, local government, and social security funds). Net issuance of debt is calculated by subtracting the redemptions of debt (paying back the face value) from the gross issuance of debt (total amount issued). When the supply of longer-term government debt rises, it is likely that prices will fall and yields will rise (when the government increases its demand for money, prices of its bonds should fall). Thus it is expected that the effect of this variable should be positive too. Data is monthly available and downloaded from the database of the Deutsche Bundesbank. Monthly values are taken as a percentage of average yearly GDP of two years.

• Asset purchases of the ECB. This is the QE variable. It shows how much worth of assets

the ECB buys under the PSPP. The ECB started QE in March 2015 and plans to allocate 88% of the total purchases to government bonds and recognized agencies and 12% to securities issued by international organizations and multilateral government banks, as

(11)

stated on the official website1. Since 88% of its purchases are aimed towards bonds, this will capture the effect on the variable of interest. The main goal of buying government bonds is to push their prices up and lower their overall yield. As stated in the beginning of this section, the component on which these asset purchases will have a greater effect is the term premium. By lowering yields on these long-term bonds borrowing becomes cheaper. This way more money will be borrowed and spent in the economy. Moreover, the supply of money in the economy also rises, which will tend to increase inflation levels. Therefore it is expected that the QE variable will be negative: QE lowers the term premium. Official data from the ECB of asset purchases in Germany is monthly available as of March 2015. Before this date this variable will take the value 0. Monthly values are taken as a percentage of 2015 GDP.

• Announcement dummy. This is a dummy variable that takes a value of 1 for January 2015

and the value of 0 elsewhere. The reason that this dummy is used is to capture the effect of the announcement of QE by the ECB. The ECB announced in January 2015 that it will implement the programme of QE in March 2015. When the announcement is made, investors expect that the QE purchases will lower the term premium and therefore this effect incorporates in the price and thus yield directly. It is expected that this variable will have a negative coefficient because investors expect the term premium to decline.

The econometric formula in symbols therefore will be the following:

T

p10_t=α+β1UGap

t+β2CPIt+β3INFdist+β4Volatilityt+β5PublicDebtt+ β6QEt+ β7Announcet+εt

•

T

p10_{t=nominal ten-year yield term premium} • UGap=Unemployment gap

• CPI=CPI inflation

• INFdis=Long-run inflation disagreement

• Volatility=Six-month realized daily volatility of the on-the-run ten year government bond • PublicDebt=Net public-sector supply of longer-term debt securities

• QE=Asset purchases of the ECB (QE)

• Announce=Announcement dummy. 1 for January 2015, 0 elsewhere.

1_{https://www.ecb.europa.eu/mopo/implement/omt/html/index.en.html}

11

(12)

Data analysis

Figure 1: Term premium

Figure 2: Unemployment gap

0 .5 1 1 .5 2 2 .5 T er m pr e m iu m m on th ly 2005m1 2010m1 2015m1 Date 0 1 2 3 4 U ne m pl oy m e nt g a p 2005m1 2010m1 2015m1 Date

The above graph shows the term premium of German government bonds in the last ten years. It can be observed that the term premium increased dramatically when the financial crisis of 2007-08 started. Investors in the markets started to require a larger term premium as a result of the economic uncertainty that the financial crisis caused.

The unemployment gap decreased dramatically from the end of 2005 to the beginning of 2009. This is because the actual unemployment rate decreased to a great extent and approached the value of the natural rate of unemployment. A possible reason for this great fall in actual

unemployment may be the Hartz reform. The Hartz reform is a list of reforms in Germany that was implemented from 2003-2005 with the purpose of improving the German labor market.

(13)

Figure 3: CPI

Figure 4: Long-run inflation disagreement

-1 -. 5 0 .5 1 C P I m o n th ly 2005m1 2010m1 2015m1 Date 1 .5 2 2 .5 3 inf l. d is a g. m on th ly 2005m1 2010m1 2015m1 Date

The CPI movements do not show any obvious trend in the last ten years. It can be seen though that in January 2015 the CPI increased with 2 percentage points. This is exactly the month when QE was announced. It is not likely though that QE succeeded in decreasing long-term yields so quickly and thus boost nominal spending in one month, so QE is not responsible for this increase. It is unknown what did cause this increase; it can be a random movement.

The above graph shows the yield on the EUR Inflation Swap Rate, which can be used as a proxy for inflation expectations.

(14)

Figure 5: Six-month realized daily volatility of the on-the-run ten year government bond

Figure 6: Net public-sector supply of longer-term debt securities

.1 .2 .3 .4 .5 6 m o nt h v ol at ilit y m on th ly 2005m1 2010m1 2015m1 Date -1 0 1 2 D eb t s up pl y % o f G DP 2005m1 2010m1 2015m1 Date

The above figure shows the six-month realized volatility of the on-the-run ten year government bond. This asset is highly traded in the market and is thus very liquid, which could explain its low standard deviation of 0.09% (see table 1).

Debt issued by the German government.

(15)

Figure 7: Asset purchases by the ECB

Results

(1) VARIABLES model 1 UGap -0.359*** (0.0476) CPI -0.156 (0.174) INFdis 0.528* (0.305) Volatility -0.0944 (0.462) PublicDebt 0.200 (0.123) QE -0.997* (0.511) Announce -0.534* (0.271) Constant 0.283 (0.665) Observations 121 R-squared 0.280

Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 0 .1 .2 .3 .4 Q E % o f GD P 2005m1 2010m1 2015m1 Date

The ECB started buying German government bonds in March 2015, which explains the flat zero-line in the graph until that date.

(16)

The coefficient of the unemployment gap turned out to be negative, meaning that a 1-percentage-point increase in the unemployment gap decreases the term premium with 36 basis points. This result is statistically significant at the 1% level. The negative coefficient is contradictory to the expected positive sign and the findings in Gagnon et al. (2010). Here a higher unemployment gap increased the term premium because investors demanded a higher compensation in times when the economy was in a bad state. A possible reason for the negative coefficient is that higher unemployment reduces spending in the economy and does not raise inflation expectations therefore. With lower inflation expectations, investors demand a lower term premium (risk premium) for inflationary risk, which would reduce their purchasing power.

The result for CPI inflation is negative as well, meaning that a 1-percentage-point increase in CPI decreases the term premium with 16 basis points. This result is also unexpected. By similar reasoning as with the unemployment gap, a higher amount of inflation would according to the adaptive expectations hypothesis raise expectations of future inflation. Investors would then demand a higher term premium. A possible explanation for this coefficient is the high p-value of 0.37 (see table 2 in appendix). The variable is insignificant at a high level, so the null hypothesis that this coefficient is equal to 0 is not rejected for high levels of significance. There is therefore not enough evidence that changes in this variable are associated in changes in the term premium. According to the regression, it is thus likely that this variable has no effect on the term premium in this model.

The coefficient of the long-run inflation disagreement turned out to be positive, as expected by economic theory. A 1-percentage-point increase in the yield of the EUR Inflation Swap Rate increases the term premium by 53 basis points. This is consistent because inflation expectations increase the term premium demanded by investors. The coefficient is however statistically insignificant at the 8% level, so at this level the null hypothesis cannot be rejected. A possible explanation for this not so low p-value is that the EUR Inflation Swap Rate represents inflation expectations of investors in all Eurozone countries, whereas the dependent variable accounts only for the term premium of German bonds.

The coefficient of the six-month realized daily volatility of the on-the-run ten year government bond turned out to be negative, which contradicts the expected positive sign. This coefficient has a very high p-value of 0.84, so it is very insignificant and cannot be used for interpretation. The null hypothesis that this value has no effect on the term premium can therefore not be rejected and it is therefore very likely that the six-month realized daily volatility of the on-the-run ten year government bond has no effect on the term premium in this model.

The coefficient of the net public-sector supply of longer-term debt securities turned out to be positive as predicted, meaning that a 1%-of-GDP increase in public debt increases the term premium with 20 basis points. This is consistent with economic theory because a higher demand for debt decreases the price and therefore increases the yield. The result is however insignificant at the 10% level, so there is some evidence that this variable might be insignificant. The variable of QE, which is the variable of interest, turned out to be significant at the 6% level with a p-value of 0.054.

A 1%-of-GDP increase in asset purchases of the ECB decreases the term premium with 100 basis points, as expected by economic theory. The coefficient turned out to be larger than in the paper of Gagnon et al. (2010). There might be a large number of possible

(17)

reasons for this difference in magnitude. The price of German bonds might for example be more sensitive to increases in demand. Another possible reason might be of different policy ideals in Germany compared to the U.S. The ECB can for example have the desire to achieve a larger decrease in the term premium than the FED. What is most important is that the policy indeed decreases the term premium. The coefficient is significant at the 6% level.

The announcement dummy turned out to be negative as expected. This means that the term premium decreased with an additional 53 basis points when QE was announced in January 2015. Investors’ expectations were therefore already incorporated in the yields when the actual implementation of QE started. This result is significant at the 6% level. Test on robustness

The situation under which the standard errors of the coefficients are constant across observations is called homoskedasticity. When this is not the case and the standard errors are unequal across values, then there is heteroskedasticity. Homoskedasticity is one of the OLS Gauss-Markov assumptions under which models have better overall quality. Estimators are under the assumption of homoskedasticity more efficient (i.e. smaller standard errors) than under heteroskedasticity, so homoskedasticity is to be preferred. Standard errors are in reality not always homoskedastic though, so a heteroskedasticity-robust regression must be run. To test whether there is homoskedasticity or heteroskedasticity, the Breusch-Pagan / Cook-Weisberg test is used with the following hypotheses:

H0: homoskedasticity H1: heteroskedasticity

The result of the test can be found in table 9 of the appendix. The p-value turned out to be 0.0533, so at the 5% level there is no evidence to assume homoskedasticity in the regression and therefore a heteroskedasticity-robust regression will be run. The p-value is not very high though, so assuming homoskedasticity might also be possible at for example a 6% level. As explained above the implication of a robust regression is that the standard errors of the estimates will be higher. Table 2 in the appendix shows the robust regression and table 3 shows the standard regression. By comparing the two regressions it can indeed be found that the standard errors of some variables are higher in table 2, but this is not the case for all variables. The coefficient of the QE variable has for example in the robust regression a lower standard error and therefore also a lower p-value, which makes the coefficient significant at a lower significance level. Figure 8 in the appendix shows a residual and fitted plot that has characteristics of heteroskedastic standard errors. The errors are for example not very symmetrical and with the fitted values of 1 to 2 there is a cluster of residuals that is higher than zero.

Test on serial correlation

When residuals in one time period are correlated with residuals in another time period, then there is serial correlation. One of the Gauss-Markov assumptions is that there is no serial correlation. The following hypotheses are tested with the Breusch-Godfrey test for serial correlation:

H0: no serial correlation H1: serial correlation

(18)

Tables 10 through 13 in the appendix show serial correlation tests for different time periods. For example table 10 shows a test for serial correlation for the last six months and table 13 shows a test for serial correlation for the last 60 months. The values are all very significant, meaning that the null hypothesis of no serial correlation of residuals is rejected. It is thus likely that there in fact serial correlation. The consequence of this problem of serial correlation is that the estimated standard errors are smaller than the true standard errors (and thus higher t-values). The model therefore looks more precise than it actually is. It is in time series data however common that that values observed in one time period will be correlated with values observed in subsequent time periods, because it is for example not likely that interest rates will exhibit jumps in observed values. This is a process that occurs gradually over time and therefore serial correlation can be expected. A possible solution would be to use an autoregressive model, but this goes beyond the scope of the paper. Therefore there should be awareness that the standard errors of the estimates in this paper are smaller than in reality.

Test on stationarity

When the variables of a time series analysis have properties that are constant over time, then they are stationary. Mean, variance, and autocorrelation are examples of such properties. When these properties are constant over time, then it is possible to use these properties for forecasting. The Augmented Dickey-Fuller test can be used to test whether variables are stationary or that they need to be differenced to make them stationary. The hypotheses of this test are therefore:

H0: the data needs to be differenced to make it stationary H1: the data is stationary and doesn’t need to be differenced

Tables 17 through 22 show the results of this test for all the explanatory variables except for the dummy variable. The tables show that the null hypothesis is rejected for UGap, CPI, Volatility, and PublicDebt. For INFdis and QE the null hypothesis is not rejected. A way to transform this data into stationary data is by differencing it. This can be done by taking for the using the change in two consecutive observations. In formula terms:

INFdis′t=INFdist−INFdist−1 QE’t=QEt-QEt-1

The data can become stationary as a result of this transformation and therefore be used for forecasting. A limitation of this model therefore is that these two variables are not stationary yet.

Model

Table 4 in the appendix shows a regression of the model without the volatility variable, which might be redundant due to a high p-value. The remaining coefficients have changed very slightly in a regression without this variable and the standard errors have decreased a bit on average. However, this is a very marginal change, so multicollinearity is not a problem in the model and it is possible to include the volatility variable as well as exclude it. The model does not become more accurate after excluding the variable.

(19)

Table 5 in the appendix shows the regression when the CPI variable with p-value 0.37 is excluded from the model. The coefficients of the model change and the standard errors do not change a lot. It is therefore not justified to exclude this variable because of a possible omitted variable bias. The F-test in table 14 shows the outcome of omitting both volatility and CPI. The high p-value shows that the null hypothesis is not rejected. The problem with omitting both volatility and CPI though is that omitted variable bias can arise. Table 6 in the appendix shows the regression without the two variables. The coefficients have visibly changed and the standard errors have not changed a lot (the model has not become more efficient). It is therefore wise to include the variables than to exclude them.

Table 15 shows the R2 of the regression in table 2. The R2 is the fraction of the sample variance of the term premium that is explained by the explanatory variables. This means that 28% of the variation in the term premium is explained by the explanatory variables. In assessing the R2_{of a model, a value of 28% is not desirable. However,} regression models in the financial world do not often have very high values of R2 _since variance in financial factors such as the term premium are very hard to explain.

It is possible that there is an important variable omitted in the model. The effects of the financial crisis that started in 2007 have not been taken into account. Data is used from 2005 to 2015, so there is a period of two years when the world was not in a financial crisis. An improvement for the model might therefore be to use a dummy variable which takes the financial crisis into account.

Another improvement might be to add a lagged dependent variable in the model. For example the term premium in the previous period can be included in the regression. This is done to account for potential omitted variables that are difficult to measure or for omitted variables for which there is no proxy. Moreover, there can be omitted variables in the model that are not known to the author of this paper or to researchers in general. Therefore including a lagged dependent variable in the model can solve for a possible omitted variable bias. The regression model then has the following equation:

T

p10_t=α+β1UGap

t+β2CPIt+β3INFdist+β4Volatilityt+β5PublicDebtt+ β6QEt+

β7Announcet+Tp10t-1+ εt

The results of this regression can be seen in table 7 of the appendix. Including a lagged dependent variable has increased the significance level at which the null hypothesis of no serial correlation cannot be rejected. The result of the Breusch-Godfrey test for serial correlation can be seen in table 16 of the appendix. The p-value of the test for 6 lags is 0.0131. Therefore at a 1% level the null hypothesis of no serial correlation cannot be rejected for 6 lags.

It can be shown in table 7 that the coefficients have changed dramatically and the R2 has increased a great deal as well compared to the original model. Since the coefficients have changed so dramatically, this suggests that there is indeed an omitted variable bias in the model of an unknown variable, so this can be concluded as a limitation of the original model.

(20)

Conclusion

This paper examined what the effect of QE is on the term premium of German bonds. According to the empirical model QE succeeded in decreasing the term premium of German bonds in the beginning phase of the programme. Further research is needed in determining whether QE keeps decreasing the term premium in subsequent months. A recommendation for other research is to estimate the effect of QE on the term premium in other European countries to compare effects of the ECB policy. Another recommendation is to examine how much effect QE has through other channels of the economy, such as the credit channel.

(21)

References:

Adrian, T., Crump, R., and Moench, E. (2013), ‘Do Treasury Term Premia Rise around Monetary Tightenings?’, Federal Reserve Bank New York, 2013(April 15).

Ball, L. (1990), ‘Why does High Inflation raise Inflation Uncertainty’, Journal of Monetary

Economics, June 1992.

Berk, J., and DeMarzo, P. (2014), ‘Corporate Finance’, Pearson.

Bernanke, B., Reinhart, V., and Sack, B. (2004), ‘Monetary Policy Alternatives at the Zero Bound: An Empirical Assessment’, Brookings Papers on Economic Activity, 2004(2). Bernanke, B. (2015), ‘Why are Interest Rates so low, part 4: Term Premiums’, January 16, 2015, http://www.brookings.edu/blogs/ben-bernanke/posts/2015/04/13-interest-rate-term-premiums.

Bernanke, B. (2012), ‘Monetary Policy since the Onset of the Crisis’, Federal Reserve Bank of

Kansas City Economic Symposium Jackson Hole, Wyoming, speech.

Bowdler, C., and Radia, A. (2012)’ Unconventional Monetary Policy: the Assessment’ Oxford

Review of Economic Policy’, volume 28(4), pp. 603-621.

Clouse, J, Henderson, D., Orphanides, A., Small, and Tinsley, P. (2000), ’Monetary Policy When the Nominal Short-Term Interest Rate is Zero’, Federal Reserve Official.

Christensen, and J., Rudebusch, G. (2012),’The Response of Interest Rates to U.S. and U.K. Quantitative Easing’, Federal Reserve Bank of San Fransisco Working Paper Series, 2012-06. Eggertsson, G., and Woodford, M. (2003), ‘The Zero Bound on Interest Rates and Optimal Monetary Policy’, Brookings Papers on Economic Activity, 2003(1).

Fawly, B., and Neely, C. (2013), ‘Four Stories of Quantitative Easing’, Federal Reserve Bank of

St. Louis Review, volume 95(1).

Gagnon, J., Raskin, M., Remache, J., and Sack, B. (2011), ’The Financial Market Effects of the Federal Reserve’s Large-Scale Asset Purchases’, International Journal of Central Banking, March 2011.

Greenwood, R., and Vayanos, D. (2010), ‘Bond Supply and Excess Bond Returns’, Review of

Financial Studies, volume 27(3).

Ji, Y., and de Grauwe, P. (2015), ‘Quantitative Easing in the Eurozone. It’s possible without Fiscal Transfers’, CESifo Area Conference on Macro, Money and International Finance, 20-21 February 2015.

(22)

Joyce, M., Lasaosa, A., Stevens,I., and Tong, M. (2011), ’The Financial Market Impact of Quantitative Easing in the United Kingdom’, International Journal of Central Banking, September 2011.

Joyce, M., Tong, M., and Woods, R. (2011), ‘The United Kingdom’s Quantitative Easing Policy: Design, Operation and Impact’, Bank of England Quarterly Bulletin, 2011 Q3. Joyce, M., Miles, D., Scott, and A., Vayanos, D. (2012), ‘Quantitative Easing and

Unconventional Monetary Policy- An Introduction’, The Economic Journal, volume 122(564). Kapetanios, G., Mumtaz, H., Stevens, I., and Theodoridis, K. (2012), ‘Assessing the Economy-wide Effects of Quantitative Easing’, The Economic Journal, volume 122(564).

Kim, D. (2007),’The Bond Market Term Premium: what is it, and how can we measure it?’,

Bis quarterly review, June 2007.

Krishnamurthy, A., and Vissing-Jorgensen, A. (2011), ‘The Effects of Quantitative Easing on Interest Rates: Channels and Implications for Policy’, Brookings Papers on Economic Activity, fall 2011.

Krishnamurthy, A., and Vissing-Jorgensen, A. (2012), ’The Aggregate Demand for Treasury Debt’, Journal of Political Economy, volume 120(2).

Mishkin, F., Matthews,K., and Giuliodori, M. (2013),’The Economics of Money, Banking, and Financial Markets’, Pearson Educated Limited.

Nelson, E. (2012), ‘Key aspects of Longer-term Asset Purchases Programs in UK and US Monetary Policy’, Oxford Economic Papers, 2013(65).

Oda, N. and Ueda,K. (2005), ‘The Effects of the Bank of Japan’s Zero Interest Rate Commitment and Quantitative Monetary Easing on the Yield Curve: A Macro-Finance Approach’, Bank of Japan Working Paper Series, no.05-E-6.

Swanson, E. (2007), ‘What we do and don’t know about the Term Premium’, FRBSF

Economic Letter, 2007(July20).

Vayanos, D. and Vila, J.L. (2009), ‘A Preferred-Habitat Model of the Term Structure of Interest Rates’, National Bureau of Economic Research, November 2009.

Wright. J. (2008), ‘Term Premiums and Inflation Uncertainty: Empirical Evidence from an International Panel Dataset’, The American Economic Review, volume 101(4).

(23)

Appendix

Table 1: summary statistics variables

Variable Obs Mean Std. Dev. Min Max Tp10 121 1.134463 .6565994 -.017 2.237476 UGap 121 .8140496 .8749101 0 3.6 CPI 121 .1198347 .3338213 -1 .9 INFdis 121 2.251685 .2632458 1.590773 2.700477 Volatility 121 .2006034 .0906841 .0782347 .513187 PublicDebt 121 .1041568 .3453813 -.7281608 2.244813 QE 121 .0247029 .0828895 0 .3335582 Announce 121 .0082645 .0909091 0 1

Table 2: detailed regression robust 1

Number of obs = 121 F( 6, 113) = . Prob > F = . R-squared = 0.2799 Root MSE = .57419 Robust

Tp10 Coef. Std. Err. t P>t [95% Conf. Interval] UGap -.3588237 .0476062 -7.54 0.000 -.4531402 -.2645071 CPI -.1563201 .1736869 -0.90 0.370 -.5004251 .1877849 INFdis .5283164 .3049781 1.73 0.086 -.0759001 1.132533 Volatility -.0944194 .4621994 -0.20 0.838 -1.01012 .821281 PublicDebt .2003939 .1230532 1.63 0.106 -.0433966 .4441844 QE -.9970609 .51116 -1.95 0.054 -2.009761 .0156394 Announce -.5336517 .2709506 -1.97 0.051 -1.070454 .0031503 _cons .2828029 .664637 0.43 0.671 -1.033963 1.599569 23

(24)

Table 3: detailed regression 1

Source SS df MS Number of obs = 121

F( 7, 113) = 6.27

Model 14.4796004 7 2.06851435 Prob > F = 0.0000 Residual 37.2551371 113 .329691479 R-squared = 0.2799

Adj R-squared = 0.2353

Total 51.7347375 120 .431122813 Root MSE = .57419

Tp10 Coef. Std. Err. t P>t [95% Conf. Interval] UGap -.3588237 .0638352 -5.62 0.000 -.4852927 -.2323546 CPI -.1563201 .1659516 -0.94 0.348 -.4851002 .17246 INFdis .5283164 .2628157 2.01 0.047 .0076312 1.049002 Volatility -.0944194 .5989916 -0.16 0.875 -1.28113 1.092291 PublicDebt .2003939 .1552121 1.29 0.199 -.1071094 .5078971 QE -.9970609 .8322077 -1.20 0.233 -2.645814 .6516926 Announce -.5336517 .6429583 -0.83 0.408 -1.807468 .7401648 _cons .2828029 .6230421 0.45 0.651 -.951556 1.517162

Table 4: detailed regression robust 2

Tp10 Coef. Std. Err. t P>t [95% Conf. Interval] UGap -.356486 .0478216 -7.45 0.000 -.4512202 -.2617517 CPI -.1557226 .1733523 -0.90 0.371 -.4991321 .1876869 INFdis .527554 .3045293 1.73 0.086 -.0757161 1.130824 PublicDebt .1974281 .1180657 1.67 0.097 -.0364591 .4313153 QE -.9955605 .51084 -1.95 0.054 -2.007531 .0164096 Announce -.5331303 .2705485 -1.97 0.051 -1.069085 .0028243 _cons .2638718 .6595885 0.40 0.690 -1.042768 1.570511 24

(25)

Table 5: detailed regression robust 3

Tp10 Coef. Std. Err. t P>t [95% Conf. Interval] UGap -.3607427 .046598 -7.74 0.000 -.453053 -.2684323 INFdis .5434732 .3044624 1.79 0.077 -.0596644 1.146611 Volatility -.0815323 .4580863 -0.18 0.859 -.9889978 .8259331 PublicDebt .1986919 .1231639 1.61 0.109 -.0452949 .4426787 QE -.9292911 .5138949 -1.81 0.073 -1.947313 .0887307 Announce -.3472672 .1904751 -1.82 0.071 -.7245969 .0300626 _cons .2258818 .6625921 0.34 0.734 -1.086708 1.538472

Table 6: detailed regression robust 4

Tp10 Coef. Std. Err. t P>t [95% Conf. Interval] UGap -.3587167 .0468865 -7.65 0.000 -.4515899 -.2658435 INFdis .5427644 .3038638 1.79 0.077 -.0591314 1.14466 PublicDebt .1961352 .1181513 1.66 0.100 -.0378998 .4301702 QE -.9282186 .5133784 -1.81 0.073 -1.945122 .0886853 Announce -.3474322 .1901717 -1.83 0.070 -.7241257 .0292612 _cons .209714 .657918 0.32 0.750 -1.093495 1.512923 25

(26)

Table 7: detailed regression 2

Source SS df MS Number of obs = 120

F( 8, 111) = 312.03

Model 49.1033688 8 6.1379211 Prob > F = 0.0000 Residual 2.1834939 111 .019671116 R-squared = 0.9574

Adj R-squared = 0.9544

Total 51.2868627 119 .430982039 Root MSE = .14025

Tp10 Coef. Std. Err. t P>t [95% Conf. Interval] UGap -.0242404 .0181689 -1.33 0.185 -.0602432 .0117624 CPI -.0510427 .0413659 -1.23 0.220 -.1330119 .0309265 INFdis .1958857 .0648999 3.02 0.003 .0672822 .3244891 Volatility .1400872 .1464229 0.96 0.341 -.1500595 .4302339 PublicDebt .0171856 .0381804 0.45 0.654 -.0584715 .0928427 QE .3768077 .2058739 1.83 0.070 -.0311452 .7847606 Announce -.0683752 .1576069 -0.43 0.665 -.3806837 .2439334 Tp10 L1. .9492105 .0225398 42.11 0.000 .9045463 .9938747 _cons -.3934205 .1531575 -2.57 0.012 -.6969122 -.0899287

Table 8: correlations

Tp10 UGap CPI INFdis Volati~y Public~t QE Announce Tp10 1.0000 UGap -0.4023 1.0000 CPI -0.0621 0.0712 1.0000 INFdis 0.2216 0.1845 0.0702 1.0000 Volatility 0.1087 -0.2284 -0.0297 0.0000 1.0000 PublicDebt 0.1303 0.0319 0.0529 0.1027 0.1156 1.0000 QE -0.1406 -0.2489 -0.0625 -0.6020 0.0177 -0.1234 1.0000 Announce -0.0762 -0.0643 -0.3075 -0.2301 -0.0019 -0.1163 -0.0273 1.0000 26

(27)

Figure 8: residual and fitted plot

Table 9: heteroskedasticity test

Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Homoskedasticity

Variables: fitted values of Tp10 chi2(1) = 3.73

Prob > chi2 = 0.0533

Table 10: serial correlation test (table 3, 6 lags)

Breusch-Godfrey LM test for autocorrelation

lags(p) chi2 df Prob > chi2

6 107.602 6 0.0000 H0: no serial correlation -1 .5 -1 -. 5 0 .5 1 R es idu al s 0 .5 1 1.5 2 Fitted values 27

(28)

Table 11: serial correlation test (table 3, 12 lags)

Table 12: serial correlation test (table 3, 24 lags)

24 109.263 24 0.0000

H0: no serial correlation

Table 13: serial correlation test (table 3, 60 lags)

60 112.265 60 0.0001

Table 14: F- test 1 (table 2)

( 1) CPI = 0

( 2) Volatility = 0 F( 2, 113) = 0.43

Prob > F = 0.6506

12 107.936 12 0.0000

(29)

Table 15: R-squared (table 2)

Number of obs = 121 F( 6, 113) = . Prob > F = . R-squared = 0.2799 Root MSE = .57419

Table 16: serial correlation test (table 7)

6 16.116 6 0.0131

Table 17: stationarity test UGap

Test 1% Critical 5% Critical 10% Critical

Statistic Value Value Value

Z(t)-4.063 -3.503 -2.889 -2.579 MacKinnon approximate p-value for Z(t) = 0.0011

Table 18: stationarity test CPI

Z(t) -14.744 -3.503 -2.889 -2.579

MacKinnon approximate p-value for Z(t) = 0.0000

(30)

Table 19: stationarity test INFdis

Test 1% Critical 5% Critical 10%

Critical

Z(t) -1.793 -3.503 -2.889 -2.579

Table 20: stationarity test Volatility

Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value

Z(t) -2.874 -3.503 -2.889 -2.579

Table 21: stationarity test PublicDebt

Test 1% Critical 5% Critical 10%

Critical

Z(t) -11.685 -3.503 -2.889 -2.579

Table 22: stationarity test QE

Z(t) -0.651 -3.503 -2.889 -2.579 MacKinnon approximate p-value for Z(t) = 0.8590